Charge-Hyperscaling Violating Lifshitz hydrodynamics from black-holes

TL;DR

This paper derives Lifshitz hydrodynamics with charge-hyperscaling violation from black hole horizons, revealing how non-equilibrium horizons relate to non-relativistic fluid dynamics with specific transport properties.

Contribution

It introduces a method to obtain Lifshitz hydrodynamics with charge-hyperscaling violation from black hole solutions, extending the holographic correspondence to non-relativistic, scale-violating theories.

Findings

Hydrodynamic equations are derived from black hole horizons with Lifshitz and hyperscaling violation.

The boundary stress tensor is computed and renormalized.

Shear viscosity to entropy ratio remains unchanged from relativistic cases.

Abstract

Non-equilibrium black hole horizons are considered in scaling theories with generic Lifshitz invariance and an unbroken U(1) symmetry. There is also charge-hyperscaling violation associated with a non-trivial conduction exponent. The boundary stress tensor is computed and renormalized and the associated hydrodynamic equations derived. Upon a non-trivial redefinition of boundary sources associated with the U(1) gauge field, the equations are mapped to the standard non-relativistic hydrodynamics equations coupled to a mass current and an external Newton potential in accordance with the general theory of [arXiv:1502.00228]. The shear viscosity to entropy ratio is the same as in the relativistic case.